Determine the linear inequality associated with the given solution. (First, find the equation of the line. Then rewrite this equation as an inequality with the appropriate inequality sign: <,>,greater than or equal to or less than or equal to
Enter the linear inequality associated with the graph on the right.
(Type an inequality. Type your answer in slope-intercept form.)
Without the graph provided, it is not possible to determine the linear inequality associated with the given solution.
1,6 6,0
To find the equation of the line passing through the points (1,6) and (6,0), we can use the slope-intercept form.
First, let's find the slope (m) of the line:
m = (Y2 - Y1) / (X2 - X1)
m = (0 - 6) / (6 - 1)
m = -6 / 5
Now that we have the slope, we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Using the point (1,6):
y - 6 = (-6/5)(x - 1)
Simplifying:
5y - 30 = -6x + 6
5y = -6x + 36
y = (-6/5)x + 36/5
To write this equation as an inequality, we need to determine whether the line is greater than or less than the points given. To do this, we can substitute the points (1,6) and (6,0) into the equation.
For (1,6):
6 = (-6/5)(1) + 36/5
6 = -6/5 + 36/5
6 = 30/5
6 = 6
For (6,0):
0 = (-6/5)(6) + 36/5
0 = -36/5 + 36/5
0 = 0/5
0 = 0
Since the equation holds true for both points, the line passes through them. Thus, the linear inequality associated with the given solution is:
y ≤ (-6/5)x + 36/5